Certification Problem

Input (TPDB SRS_Standard/Waldmann_19/random-397)

The rewrite relation of the following TRS is considered.

b(a(a(b(x1)))) b(b(b(b(x1)))) (1)
b(b(b(a(x1)))) b(b(b(b(x1)))) (2)
a(b(b(b(x1)))) b(a(a(a(x1)))) (3)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Rule Removal

Using the Knuth Bendix order with w0 = 1 and the following precedence and weight functions
prec(a) = 1 weight(a) = 2
prec(b) = 0 weight(b) = 2
all of the following rules can be deleted.
b(a(a(b(x1)))) b(b(b(b(x1)))) (1)
b(b(b(a(x1)))) b(b(b(b(x1)))) (2)
a(b(b(b(x1)))) b(a(a(a(x1)))) (3)

1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.